a széken – on the chair
a székre – onto the chair
a székről – from the chair

Like in the previous case, these can agree with different English prepositions. Understanding the Hungarian point of view is the only help you can count on. However, like I said before, once understood, you’ll see it’s absolutely logical. The suffix -n is used with words in a vowel.

The vowels a, e become á, é in those words: fa, gereblye

a fán – on the tree
a fára – onto the tree
a fáról – from the tree

a gereblyén – on the rake
a gereblyére – onto the rake
a gereblyéről – from the rake

Examples in sentences:

Az asztalon van a toll. – The pen is on the table.
Az asztalra teszem a tollat. – I’ll put the pen on(to) the table.
Az asztalról leesik a toll. – The pen falls from the table.

A széken van a táska. – The bag is on the chair.
A székre teszem a táskát. – I’ll put the bag on(to) the chair.
A székről leesik a táska. – The bag falls from the chair.

A fán énekel a madár. – The bird is singing on the tree.
A fára száll a madár. – The bird flies on(to) the tree.
A fáról elrepül a madár. – The bird flies away from the tree.

A gereblyén tücsök ciripel. – A cricket’s chirping on the rake.
A gereblyére tücsök ugrik. – A cricket jumps on(to) the rake.
A gereblyéről leugrik a tücsök. – The cricket jumps from the rake.

The difference between -ra, -re and -n, -on, -en, -ön:

Felmászok a hegyre. – I climb up(to) the mountain.
A hegyensétálok. – I’m walking on the mountain.

Summary for suffixes on the surface of an object:-ra, -re = towards a direction-n, -on, -en, -ön = position > something is to be found somewhere-ról, -ről = from a direction

As you see some suffixes have two versions for high and deep, some have three. Learn the suffixes as you see here. There is no ö version (-bön) for -ban, -ben or an a version (-bal) for -ból, -ből. They have to be memorized as they are. For example -ből is used for standard high words and words having ö ő ü ű. However, -en is for standard high words, -ön is for high words containing ö ő ü ű. And so on…

What I mean by that is: DON’T INVENT SUFFIXES JUST BECAUSE IT WOULD AGREE WITH VOWEL HARMONY. There are only the versions you see here.